Question

The value of $\frac{\sqrt{7}+2}{\sqrt{7}-2}+\frac{\sqrt{7}-2}{\sqrt{7}+2}$ is $\frac{8\sqrt{7}}{m}$, then the value of$m$ is ?

Answer 1

$\frac{\sqrt{7}+2}{\sqrt{7}-2}+\frac{\sqrt{7}-2}{\sqrt{7}+2}=\frac{(\sqrt{7}+2)(\sqrt{7}+2)+(\sqrt{7}-2)(\sqrt{7}-2)}{(\sqrt{7}+2)(\sqrt{7}-2)}=\frac{8\sqrt{7}}{3}$

on comparing $\frac{8\sqrt{7}}{m}$ by our answer we get $m=3$